(a)[5]
Express $f(x)$ as partial fractions.
(b)[5]
Hence show that $\int_{0}^{2} f(x)\,dx = \ln 54 - \dfrac{1}{8}\pi$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Let $f(x)$ be defined by $f(x) = \dfrac{5x^2 + x + 11}{(4 + x^2)(1 + x)}$.
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This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or imply the form $\dfrac{Ax+B}{4+x^2}+\dfrac{C}{1+x}$.” …
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